Oblique Confinement and Phase Transitions in Chern-Simons Gauge Theories

TL;DR

This paper explores phase transitions in a lattice-formulated Chern-Simons gauge theory relevant to quantum Hall systems, revealing an oblique confinement phase and a transition to Coulomb or confinement phases based on excitation gap size.

Contribution

It introduces a lattice formulation of the Chern-Simons gauge theory and identifies the oblique confinement phase as modeling the incompressible quantum fluid in quantum Hall systems.

Findings

Identification of oblique confinement phase for large gap M

Phase transition to Coulomb or confinement phase for smaller M

Correlation between electromagnetic coupling and phase behavior

Abstract

We investigate non-perturbative features of a planar Chern-Simons gauge theory modeling the long distance physics of quantum Hall systems, including a finite gap M for excitations. By formulating the model on a lattice, we identify the relevant topological configurations and their interactions. For M bigger than a critical value, the model exhibits an oblique confinement phase, which we identify with Lauglin's incompressible quantum fluid. For M smaller than the critical value, we obtain a phase transition to a Coulomb phase or a confinement phase, depending on the value of the electromagnetic coupling.